PROOF DWT Photovoltaic reverse osmosis Feasibility and a pathway to develop technology. Desalination and Water Treatment

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1 Desalination and Water Treatment / Desalination Publications. All rights reserved. doi: /dwt xx (2011) month PROOF DWT 7992 Photovoltaic reverse osmosis Feasibility and a pathway to develop technology Amy M. Bilton a *, Leah C. Kelley b, Steven Dubowsky b a Department of Aeronautics and Astronautics, b Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Tel.??; Fax??; bilton@mit.edu Received 13 October 2010; Accepted in revised form 7 December 2010 ab s t r ac t Small-scale photovoltaic-powered reverse osmosis (PVRO) desalination plants can provide fresh water to remote communities that do not have sufficient natural sources. For these systems to be practical, they must be both technically and economically feasible. This paper presents a research program that is focused on improving the feasibility of PVRO systems. As the first step in this program, a methodology to evaluate the economic feasibility was developed. The results, reviewed here, show that the economic feasibility is a strong function of location. The results also show that increasing the efficiency of PVRO systems can extend their feasibility to currently marginal or unfeasible locations. A focus of this research program is the development of smart control algorithms to increase system efficiency and improve feasibility. This paper presents PVRO system models which have been developed to evaluate the smart control algorithms. These models are verified using an experimental system also described here. Early experimental results are presented that show good agreement with the analytical models. Keywords:?? 1. Introduction 1.1. Motivation Approximately 1.2 billion people worldwide do not have access to adequate clean water [1]. Many of these people live in small remote communities off of the main water grid. That number will increase with population growth and global warming [2,3]. Alternative water solutions are required for these locations. Remote communities are often located in areas with access to seawater or brackish groundwater. For such * Corresponding author. communities, small scale reverse osmosis (RO) desalination can provide fresh water. Desalination is an energy intensive process. Diesel generators or grid power are commonly used to power RO systems; however, diesel generators pollute the environment and their fuel is expensive. Grid power may not be available or may be expensive. Using photovoltaics to power RO desalination systems is a promising solution for such communities. Here, the economic feasibility of photovoltaic reverse osmosis (PVRO) systems is briefly reviewed. From these results it is clear that a key to extending the utility of PVRO is improving its efficiency. This paper then presents our research program s pathway to meet this objective. Presented at EuroMed 2010 Desalination for Clean Water and Energy: Cooperation among Mediterranean Countries of Europe and MENA Region, 3 7 October 2010, David Intercontinental Hotel, Tel Aviv, Israel. Organized by the European Desalination Society.

2 2 A.M. Bilton et al. / Desalination and Water Treatment xx (2011) Background and literature review There are well-established desalination technologies to produce water for large communities, such as reverse osmosis and thermal desalination. Thermal processes work well for large communities, but they do not scale well for smaller communities. Reverse osmosis desalination systems can be scaled more easily for the demands of smaller communities. PVRO systems have been proposed [4 8]. Early systems simply combined a photovoltaic array and batteries to power an existing reverse osmosis desalination system. Battery-based systems were found to be inefficient and expensive. Recent research has focused on increasing system efficiency with some success [4,5]. Photovoltaicpowered reverse osmosis systems without batteries have also been the subject of significant research [6,7]. These studies show that PVRO systems are technically feasible. However, for PVRO to be practical, it must be economically competitive with alternative, conventional methods. In this research program, the economic feasibility of PVRO systems for small communities has been studied [9]. The results of this study, summarized in Section 2, show the current efficiency of these systems limit the use of PVRO for many communities Overview of the research program Increasing overall PVRO system efficiency can potentially increase the locations where PVRO systems are practical. Substantial research is being done to improve the efficiency of individual system components, such as solar cells and reverse osmosis membranes; however, little research is currently being done on optimizing the overall system performance using system control methods. One of the major challenges associated with the control of small-scale PVRO systems is accommodating variations in the solar radiation. This variation requires the system to adjust its settings to maintain its maximum water production. Variations in other system factors, such as air temperature, water temperature, and water source salinity, also require adjustments to the system. The common solution for dealing with variations in solar radiation is to include batteries to store energy; however, batteries are expensive and have limited lives. The approach taken here will consider system configurations without batteries. The system operation must be adjusted continuously to maximize water output while maintaining water quality and prolonging system component lives. Autonomous control is also required, since it is not practical for an operator to monitor a small-scale PVRO system continuously. To achieve these objectives, a series of PVRO system models, described below, have been developed to evaluate system and control algorithm performance. A small-scale experimental system has been designed and fabricated to validate the system models and evaluate control approaches. Details of the system design and sample experimental data are presented. The system models show good agreement with preliminary experimental results. 2. Feasibility study A feasibility study was conducted as a first step in this research program [9]. As discussed above, PVRO systems have been developed and shown to be technically feasible. To be practical, however, these systems must also be economically feasible. Economic feasibility studies of PVRO systems have been conducted in the past for specific locations, such as Oman, Greece and the United Arab Emirates [10 12]. Studies of these results show that feasibility of PVRO systems is critically dependent on location. A generalized method to determine economic feasibility as a function of location had not yet been done. In our feasibility study, a generalized method to evaluate the economic feasibility of small-scale PVRO systems as a function of location is developed. The economic feasibility is determined by comparing the PVRO water cost with that of water provided by conventional methods. The common methods to provide fresh water to remote, water scarce regions is by transporting water or by using diesel powered water desalination. Feasible regions are those where the cost of water produced by the PVRO system is less than the cost of transported water, and the total system lifetime cost of the PVRO system is less expensive than an equivalent diesel-powered reverse osmosis system. To determine economic feasibility, the full lifecycle costs of both the photovoltaic-powered and dieselpowered reverse osmosis systems were calculated. The lifecycle costs were broken into two components: the system capital costs and operating costs. These costs are determined for a location based on the local solar resource, water characteristics and water demands. A simple schematic of the PVRO system considered is shown in Fig. 1. (The difference between the PVRO and diesel generator system is the power source; otherwise a schematic for the diesel system is identical.) Here, the energy source powers a feed pump and a high-pressure pump to pressurize the incoming water. The high pressure produced by the pumps drive the water through the reverse osmosis membrane, leaving high pressure brine that passes through a turbine to recover its energy before exiting the system. An energy analysis was performed to determine the reverse osmosis system capacity, solar array size, diesel generator size and diesel fuel consumption rate for a given water production and location. Since it was assumed that the photovoltaic-powered system does not have batteries, it only runs during the daytime. The diesel-powered system is assumed to run 24 h/d. Local political factors, such as incentives and carbon taxes are not included. The

3 A.M. Bilton et al. / Desalination and Water Treatment xx (2011) Fig. 1. Simple photovoltaic reverse osmosis system considered in evaluation. cost of water produced by the diesel-powered and PVRO systems was then determined using the equivalent annualized cost method [13]. The PVRO system is considered economically feasible if the calculated water cost is less than the cost of water produced by the diesel-powered system and that of transported water [9]. Geographic Information Systems (GIS) data of annual solar insolation [14] and water characteristics [15] are used in the analysis. Cost data, component lifetimes and maintenance schedules are taken from the published literature. The key parameters for the cost analysis are shown in Table 1 [9]. The overall water cost for the PVRO systems is shown in Fig. 2. The majority of the equatorial regions are able to produce water for less than $6.00/m 3. PVRO systems are able to produce water at a cost of less than $5.00/m 3 in many water-stressed areas, such as the Middle East. The regions where the PVRO system is more cost effective than the diesel-powered system are shown in Fig. 3, and include large areas of water scarce regions. The coastal regions of northern Africa, the Middle East, South Africa, Mexico and the Caribbean are all examples of water stressed areas where a seawater PVRO system could feasibly deliver clean water to small communities at a lower cost than diesel-powered reverse osmosis systems. Table 1 Input parameters for seawater reverse osmosis analysis [9] Parameter Value Plant capacity 10 m 3 Plant lifetime 25 years Interest rate 5% Plant capacity factor 90% Recovery ratio 40% Reverse osmosis system cost [13] $2400/m 3 Installed array system cost [16] $9.00/Wp Initial diesel fuel cost [17] $0.66/L ($2.50/gallon) Fig. 2. Cost of water ($/m 3 ) for solar powered system [9]. Fig. 3. Areas where a solar powered system is less expensive than a diesel system without government incentives [9]. Table 2 shows the details for six representative locations. As expected, the areas with higher water salinity require more energy to perform reverse osmosis, and the areas listed with the low solar insolation are not favorable for the solar powered systems. For the price assumptions made, the PVRO system is less expensive than the diesel system for all of the sites except Boston and Los Angeles. In general, PVRO is feasible in areas with a high solar resource. The results of the study show the clear location dependency of PVRO feasibility. This dependency is due to the

4 4 A.M. Bilton et al. / Desalination and Water Treatment xx (2011) Table 2 Site specific analysis results seawater reverse osmosis without incentives and carbon tax [9] Location Boston, USA Los Angeles, USA Limissol, Cyprus Aqaba, Jordan Cap-Haïtien, Haiti Jeddah, Saudi Arabia Latitude N N N N N N Longitude W W E E 72.2 W E Average latitude tilt solar insolation (kwh/m 2 -d) Daylight hours (h) Water salinity (ppm) Energy required per day (kwh) Solar array area (m 2 ) Total PVRO system capital cost ($) 149, , , , , ,748 PVRO system equiv. annual cost ($) 21,757 17,524 16,568 17,265 16,523 15,447 Total diesel system capital cost ($) 46,718 46,644 46,362 46,279 46,497 46,445 Diesel system equiv. annual cost ($) 17,147 17,295 17,983 18,231 17,626 17,758 Cost of water solar ($/m 3 ) Cost of water diesel ($/m 3 ) differences in water demand, water characteristics and solar resources. They also show that the PVRO is feasible for many water-stressed regions. The high fuel costs for the diesel-powered systems result in higher water costs for most locations. When the system is configured for a region without high solar resource, the high capital costs for community-scale seawater PVRO systems are not recovered during the system lifetime. With intelligent system control of the PVRO systems, it is possible to further reduce system costs, thus the PVRO systems could become affordable for larger regions. 3. System modeling Full non-linear system models have been developed for PVRO systems. The models incorporate the key factors that affect PVRO system performance, including solar radiation, water salinity, water temperature, air temperature and water demand. A representative PVRO system with stochastic system inputs is shown in Fig. 4. The PVRO system models have been developed in Fig. 4. PVRO system schematic. Matlab/Simulink. A high-level block diagram of a simple PVRO system is shown in Fig. 5. These models were constructed at the individual component level, and are Fig. 5. High-level PVRO system model block diagram.

5 A.M. Bilton et al. / Desalination and Water Treatment xx (2011) a blend of physics-based and empirical equations. Full presentation of all model equations is beyond the scope of this paper. Here, only the key concepts are presented Solar energy model A simple model was developed to estimate the solar energy available during a clear day. For a given latitude, longitude and time, the solar elevation and azimuth are well-known [18]. This model is used to estimate the direct, diffuse and reflected portions of solar radiation [19]. Then, the amount of direct radiation incident on the panel can be found using the following equation: Gmod,dir = Gdir cos α sinβcos( ψ θ ) + sin α cosβ (1) where G dir is the direct insolation on a plane normal to the incoming sun rays, α is the sun elevation angle, β is the module tilt angle, ψ is the module azimuth angle, and θ is the azimuth angle of the sun. The total insolation incident on the panel surface is given by: Gmod,dir = Gmod,dir + Gmod,dif + Gmod,ref (2) where G mod,dif and G mod,ref are the diffuse and reflected radiation received by the panel, respectively Solar array model For the PV panel, each individual solar cell is represented using the classic two-diode model, given by [20]: V + I R cell s cell = ph D1 D2 (3) Rsh I I I I where I cell is the cell current, I ph represents the light generated current, I D1 and I D2 represent the losses due to recombination (which are temperature dependent), V is the solar cell operating voltage, R s is the solar cell series resistance in ohms, and R sh is the solar cell shunt resistance in ohms. The light-generated current is given by: ( ) I = A C + C T G (4) ph c 0 1 cell mod,tot where A c is the solar cell area in m 2, C 0 and C 1 are solar cell-specific constants, T cell is the cell temperature in Kelvin, and G mod,tot is the incoming solar radiation in W/m 2. The cell temperature at a given solar radiation is given by the following empirical relationship: T cell Gmod,tot ( NOCT ) = Tamb + (5) 800 where T amb is the ambient temperature in Kelvin, NOCT is the normal operating cell temperature in Kelvin, and G mod, tot is the total incident solar insolation on the module in W/m 2. The solar panel model was developed by connecting the individual solar cell models into strings in series, and then connecting the strings in parallel. In this model, all cells are assumed identical. For the series connections, the current through all of the cells is the same and the voltage adds, so Eq. (3) applies. Voltage V string and current I string for cells connected in a series string are found using: Vstring = ncellvcell (6) I string = I (7) cell where n cell is the number of cells connected in the string. For the parallel string connections, the voltage remains the same and the currents add. This relationship is expressed as follows: Imodule = nstringistring (8) V module = V (9) string where I module is the current of the module, V module is the module voltage, and nstring is the number of strings connected in parallel Control electronics The control electronics and computer take the power being produced by the solar array and condition it for use by the reverse osmosis system motors and pumps. In this portion of the model, different control algorithms can be implemented to control the operating point of the PVRO system. Since the systems considered here do not use batteries and the power conversion is not perfect, the following relationship is used: VmotorImotor = η mpptvmoduleimodule (10) where V motor is the motor voltage, I motor is the motor current and η mppt is the power conversion efficiency from the solar module to the motor, and V module and I module are the voltage and current of the solar module found from Eqs. (8) and (9) Motor A simple static motor model, with motor resistance assumed constant, was used to estimate the system performance. The shaft torque τ can be expressed using the following equation: ( ) τ = I I / K (11) motor 0 T where I motor is the motor current, I 0 is the friction related current, and K T is the torque constant. The internal back-emf, V m is assumed to be proportional to the rotor speed Ω via the motor speed constant K V as shown: V m = Ù / K (12) V

6 6 A.M. Bilton et al. / Desalination and Water Treatment xx (2011) The motor terminal voltage V motor can be found by adding the resistive voltage drop to the back-emf, V m as shown: Ù V = V + I R = + I R (13) motor m motor m motor m KV where R m is the resistance of the motor in Ohms Pump Due to the pressures and flow rates involved in the reverse osmosis system, positive displacement pumps are commonly used. The flow rate produced by a positive displacement pump Q is found using: D p Q = Dn cs Q 2π µ R (14) where n is the pump speed in revolutions per minute, D is the pump volumetric displacement per revolution, c s is the pump slip coefficient, μ is the dynamic viscosity of the water, Δp is the pressure difference across the pump, and Q R is the flow loss due to inlet flow restriction. The torque required by a positive displacement pump is given by: pd D τ = cddµ n + cf p + Tc 2 π 2 π (15) where c d is the coefficient of viscous drag, c f is the coefficient of friction for the pump geometry, and T c is the pump torque constant. Since the motor and pump share the same shaft, the speed and torque of the motor and pump are identical Energy recovery There are many different types of reverse osmosis energy recovery devices. The presentation of the full set of equations describing the energy recovery is beyond the scope of this paper. For full details, refer to [6]. Here, the Clark Pump pressure exchanger produced by Spectra Watermakers [5] is described. The Clark pump is a fixed-ratio pressure exchanger consisting of two pistons connected with a rod, as shown in Fig. 6. When the piston reaches the end of travel, a reversing valve switches the brine and exhaust connections, and the piston reverses direction. The area of the rod changes the effective areas on either side of the piston, and the device adds the energy in the medium pressure feed to the energy in the concentrate, producing water at a higher pressure than the concentrate. The recovery ratio, R t, of a reverse osmosis system using the Clark pump is defined as [6]: R A Q = r p t A = p Q (16) f Fig. 6. Basic Clark pump mechanics. where A p is the area of the piston, A r is the area of the connecting rod, Q p is the fresh water flow rate, and Q f is the medium pressure feed flow rate. Using the recovery ratio, the relationships for the fresh water flow rate Q P and brine flow rate Q E, respectively, are [6]: QP = RtQF QL (17) ( 1 ) Q = Q R + Q (18) E F t L where Q L are the leakage flow rates in the Clark pump, found empirically using [6]: Q = Q P (19) 4 5 L F H where P H is the pressure of the feed water entering the RO pressure vessel. The feed water pressure is found by balancing the forces on the piston, and can be defined in terms of the recovery ratio as [6]: ( 1 ) ( 1 ) P = P + P R R P (20) H F C t t L where P F is the pressure of the feed water entering the Clark pump, P C is the pressure of the brine entering the pump, P E is the pressure of the brine exiting the pump, and P L are the pressure losses in the pump. The pressure losses are defined empirically using [6]: P = 49.2Q P (21) L 2 2 f where Q f is the feed flow rate in L/s and ΔP = P H P C in bar Reverse osmosis membrane An RO membrane is a cross-flow separator. The flow of fresh water out of the membrane can be written as: Qp = ASE(TCF)(FF)( P π ) (22) where S E is the membrane surface area, A is the membrane permeability for water, TCF is the water permeability temperature correction factor, FF is the membrane fouling factor, P is the average pressure applied across the membrane, and π is the average osmotic pressure applied across the membrane. Here, empirical relations from Dow [21] are used to determine the temperature

7 A.M. Bilton et al. / Desalination and Water Treatment xx (2011) correction factor, and the fouling factor is not currently estimated. The average pressure applied across the membrane is found using: Pfc P = PH P (23) p 2 where P p is the pressure of the fresh water exiting the membrane and ΔP fc is the pressure drop over the membrane module, estimated empirically using [21]: 1.7 QC + QF Pfc = (24) where Q C and Q F are the brine and feed flow rates in L/s, respectively. The pressure drop over the membrane can also be used to calculate the pressure in the exiting brine using: PC = PH Pfc (25) The average difference in osmotic pressure is calculated using: π f + πb π = ( pf ) π (26) p 2 where pf is the concentration polarization factor, π f is the osmotic pressure of the feed, π b is the osmotic pressure of the brine, and π p is the osmotic pressure of the fresh water. The osmotic pressure is estimated using an empirical relationship from the ASTM Standards [22], and the polarization factor is estimated using an empirical relationship derived by Dow [21]. Since separation across an RO membrane is not perfect, some salt is also transmitted across the membrane in the fresh water. The concentration of salt in the fresh water is given by: C p BSE ( pf )( TCF) Ccf = (27) Q p in Matlab/Simulink using the structure shown in Fig. 5. The ode45 solver is used to simultaneously solve the system of equations. This complete model forms the core of our optimal control algorithm development. To ensure that these models are sound, they are validated with our experimental system, described below. 4. Experimental system The MIT system has been constructed on a campus rooftop (see Fig. 7). This system is modular and reconfigurable. It is composed of a tracking PV panel, custom control electronics, parallel DC pumps, a Clark pump energy recovery system, reverse osmosis membrane within a pressure vessel, and plastic water tanks. The system does not use batteries for power leveling. Small batteries are used as backup power for the electronics. The system is fully instrumented and computer controlled to optimize the system water output, and is designed to produce approximately 300 L of fresh water per day in Boston on a sunny summer day. The system instrumentation consists of 18 different sensors that provide sufficient information for model validation and control feedback (see Fig. 8). Sensors include thermistors for measuring solar panel, feed water, and ambient air temperature, flow sensors, salinity sensors, pressure transducers, and sensors for measuring solar panel orientation. The sensors are connected via custom electronics to the data acquisition and control computer, shown in Fig. 9. Two PIC24 microcontrollers in a Master/Slave configuration are used to acquire sensor data through a sensor conditioning board, and to perform computation and where B is the membrane permeability to salt and C fc is the average concentration of the water on the concentrate side of the membrane, given by: C C + C 2 f b fc = (28) where C f is the salt concentration in the feed water and C b is the salt concentration in the exiting brine. Finally, since salt water flow is considered incompressible, the flow of both water and salt are conserved: QF = QC + Qp (29) QFCf = QCCb + QpC (30) p Eqs. (1) (30) are a complex set of nonlinear quasistatic equations whose solution has been implemented Fig. 7. Experimental system setup.

8 8 A.M. Bilton et al. / Desalination and Water Treatment xx (2011) Fig. 8. Experimental system layout. Fig. 9. Experimental system data acquisition, control and power architecture. control tasks. The Master PIC24 is used to control a DC/ DC step down converter that receives power from the solar panels and converts it to the voltage desired by the two DC boost pumps. The Slave PIC24 is used to drive the solar panel tracker motors. The Master PIC24 also communicates with a base station PC running Linux over a wireless modem. The base station is used to record the acquired data and to display it in real time. A model of the experimental system was developed using the framework outlined in Section 3 above. The system parameters for this model of the experimental system are shown in Table 3. These parameters were determined through manufacturer-supplied data and component characterization. The experimental system has been tested under a variety of different weather conditions using a simple

9 Table 3 Experimental system model parameters A.M. Bilton et al. / Desalination and Water Treatment xx (2011) Component Parameter Value Sunpower 230W solar panel [23] Solar cell area, A c Light current constant, C A/W Light current temperature dependence constant, C A/W-K Normal operating cell temperature, NOCT 45 C Number of solar cells connected in a string, n cell 72 Number of strings connected in parallel, n string 1 Solar cell series resistance, R s Ω Solar cell shunt resistance, R sh 1296 Ω Shurflo pump & motor Pump coefficient of viscous drag c d N-m/bar-L Pump friction coefficient, c f N-m/bar-L Pump slip coefficient, c s Pump volumetric displacement per revolution, D L/rev Motor friction related current,i A Motor torque constant, K T A/N-m Motor speed constant, K V rev/v-s Motor resistance, R m Ω Pump torque constant, T c 0.05 Nm DOW Filmtec SW reverse osmosis Membrane water permeability, A L/m 2 -bar-s membrane [24] Membrane salt permeability, B L/m 2 -s Membrane area, S E 2.8 m 2 Other system parameters Feed water salt concentration, C f mg/l Clark pump recovery ratio, R t conventional maximum power point tracking control. Here, data from a partly day is used to validate the system models. The experimental system model outlined above was simulated for the mostly sunny day using the data collected for solar radiation (shown in Fig. 10), ambient temperature, water salinity, and water temperature as inputs. Fig. 11 shows the water production predicted by the model and the experimentally measured water produc- tion. The predicted and experimentally measured results agree well, with a difference of 5% between measured and predicted performance. As expected, the system produced approximately 300 L of clean water. The overall experimental reverse osmosis system efficiency was also calculated and compared to the modeled results (see Fig. 12). The model agrees well with the experimental data. The overall specific energy consumption of the experimental system ranges between Fig. 10. Solar radiation incident on solar panel. Fig. 11. Water produced over course of the day.

10 10 A.M. Bilton et al. / Desalination and Water Treatment xx (2011) Fig. 12. Overall reverse osmosis system efficiency. 4 kwh/m 3 and 2.5 kwh/m 3 when there is a reasonable input power available. 5. Conclusions This paper has presented the motivation for the PVRO control research currently being conducted. A feasibility study was performed, which found that the geographic regions where PVRO is cost effective for small, remote communities can be increased by improving overall system efficiency, and that research in improved total system efficiency using smart control techniques is needed. Experimentally validated system models of small-scale PVRO systems have been developed for use for control algorithm design. Preliminary experimental results show good agreement with the models. Acknowledgements The authors would like to thank the King Fahd University of Petroleum and Minerals in Dhahran, Saudi Arabia, for funding the research reported in this paper through the Center for Clean Water and Clean Energy at MIT and KFUPM. The authors acknowledge efforts of KFUPM Team members in this joint collaborative research. The authors would also like to thank the Cyprus Institute for their fellowship support of Ms. Bilton. Symbols A Reverse osmosis membrane water permeability, L/m 2 -bar-s A c Solar cell area, m 2 A p Area of the Clark pump piston, m 2 A r Area of the Clark pump connecting rod, m 2 B Reverse osmosis membrane salt permeability, L/m 2 -s Brine salt concentration, mg/l C b C f Feed water salt concentration, mg/l C fc Average concentration of the water on the concentrate side of the membrane, mg/l C 0 Solar cell-specific light current constant, 1/V C 1 Solar cell-specific light current temperature dependence constant, 1/V-K c d Pump coefficient of viscous drag, N-m/bar-L c f Pump geometry friction coefficient, N-m/bar-L c s Pump slip coefficient, Pa/bar D Pump volumetric displacement per revolution, L/rev FF Reverse osmosis membrane fouling factor G dir Direct solar radiation in plane normal to incoming rays, W/m 2 G mod,dif Diffuse panel radiation, W/m 2 G mod,ref Reflected panel radiation, W/m 2 G mod,tot Total panel incident solar radiation, W/m 2 I cell Total solar cell current, A I D1 Solar cell current losses due to recombination in bulk material, A I D2 Solar cell current losses due to recombination in space charge region, A I module Solar module current, A I motor motor current, A I ph Solar cell light generated current, A I string Current produced by string solar cells, A I 0 Motor friction related current, A K T Motor torque constant, A/N-m K V Motor speed constant, rev/v-s NOCT Normal solar cell operating temperature, K n Pump speed, rev/s n cell Number of solar cells connected in a string n string Number of strings connected in parallel P C Pressure of brine entering the Clark pump, bar P E Pressure of brine exiting the Clark pump, bar P F Feed water pressure entering Clark pump, bar P H Pressure of the feed water entering the RO pressure vessel, bar P L Clark pump pressure losses, bar P p Permeate pressure, bar p f Membrane concentration polarization factor Q Pump flow rate, L/s Q C Clark pump entering brine flow rate, L/s Q E Clark pump exiting brine flow rate, L/s Q F Medium pressure feed flow rate, L/s Q L Clark pump leakage flow rate, L/s Q R Flow loss due to pump inlet flow restriction, L/s Q p Permeate flow rate, L/s R m Motor resistance, Ω R s Solar cell series resistance, Ω R sh Solar cell shunt resistance, Ω R t Clark pump recovery ratio S E Reverse osmosis membrane surface area, m 2 T amb Ambient temperature, K Pump torque constant, Nm T c

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